Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-19T21:33:29.841Z Has data issue: false hasContentIssue false
  • English
  • Français

Efficient Kriging surrogate modeling approach for system reliability analysis

Published online by Cambridge University Press:  04 May 2017

Zhen Hu ,
Saideep Nannapaneni  and
Sankaran Mahadevan
Zhen Hu
Affiliation:
Department of Civil & Environmental Engineering, Vanderbilt University, Nashville, Tennessee, USA
Saideep Nannapaneni
Affiliation:
Department of Civil & Environmental Engineering, Vanderbilt University, Nashville, Tennessee, USA
Sankaran Mahadevan*
Affiliation:
Department of Civil & Environmental Engineering, Vanderbilt University, Nashville, Tennessee, USA
*
Reprint requests to: Sankaran Mahadevan, Department of Civil & Environmental Engineering, Vanderbilt University, Box 1831, Station B, Nashville, TN 37235, USA. E-mail: sankaran.mahadevan@vanderbilt.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Current limit state surrogate modeling methods for system reliability analysis usually build surrogate models for failure modes individually or build composite limit states. In practical engineering applications, multiple system responses may be obtained from a single setting of inputs. In such cases, building surrogate models individually will ignore the correlation between different system responses and building composite limit states may be computationally expensive because the nonlinearity of composite limit state is usually higher than individual limit states. This paper proposes a new efficient Kriging surrogate modeling approach for system reliability analysis by constructing composite Kriging surrogates through selection of Kriging surrogates constructed individually and Kriging surrogates built based on singular value decomposition. The resulting composite surrogate model will combine the advantages of both types of Kriging surrogate models and thus reduce the number of required training points. A new stopping criterion and a new surrogate model refinement strategy are proposed to further improve the efficiency of this approach. The surrogate models are refined adaptively with high accuracy near the active failure boundary until the proposed new stopping criterion is satisfied. Three numerical examples including a series, a parallel, and a combined system are used to demonstrate the effectiveness of the proposed method.

Keywords

KrigingReliability AnalysisSingular Value DecompositionSystem
Type
Special Issue Articles
Information
AI EDAM , Volume 31 , Special Issue 2: Uncertainty Quantification for Engineering Design , May 2017 , pp. 143 - 160
Copyright
Copyright © Cambridge University Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Basudhar, A., & Missoum, S. (2008). Adaptive explicit decision functions for probabilistic design and optimization using support vector machines. Computers & Structures 86(19), 1904–1917.CrossRefGoogle Scholar
Basudhar, A., Missoum, S., & Sanchez, A.H. (2008). Limit state function identification using support vector machines for discontinuous responses and disjoint failure domains. Probabilistic Engineering Mechanics 23(1), 1–11.Google Scholar
Bichon, B.J., Eldred, M.S., Swiler, L.P., Mahadevan, S., & McFarland, J.M. (2008). Efficient global reliability analysis for nonlinear implicit performance functions. AIAA Journal 46(10), 2459–2468.CrossRefGoogle Scholar
Bichon, B.J., McFarland, J.M., & Mahadevan, S. (2011). Efficient surrogate models forreliability analysis of systems with multiple failure modes. Reliability Engineering & System Safety 96(10), 1386–1395.Google Scholar
Bishop, C.M. (1995). Neural Networks for Pattern Recognition. Oxford: Oxford University Press.Google Scholar
Chatterjee, A. (2000). An introduction to the proper orthogonal decomposition. Current Science 78(7), 808–817.Google Scholar
Choi, S.-K., Grandhi, R.V., Canfield, R.A., & Pettit, C.L. (2004). Polynomial chaos expansion with latin hypercube sampling for estimating response variability. AIAA Journal 42(6), 1191–1198.CrossRefGoogle Scholar
Dey, A., & Mahadevan, S. (1998). Ductile structural system reliability analysis using adaptive importance sampling. Structural Safety 20(2), 137–154.Google Scholar
Du, X., & Chen, W. (2002). Efficient uncertainty analysis methods for multidisciplinary robust design. AIAA Journal 40(3), 545–552.Google Scholar
Du, X., & Chen, W. (2004). Sequential optimization and reliability assessment method for efficient probabilistic design. Journal of Mechanical Design 126(2), 225–233.CrossRefGoogle Scholar
Du, X., & Sudjianto, A. (2004). First order saddlepoint approximation for reliability analysis. AIAA Journal 42(6), 1199–1207.Google Scholar
Echard, B., Gayton, N., & Lemaire, M. (2011). AK-MCS: an active learning reliability method combining Kriging and Monte Carlo simulation. Structural Safety 33(2), 145–154.CrossRefGoogle Scholar
Echard, B., Gayton, N., Lemaire, M., & Relun, N. (2013). A combined importance sampling and kriging reliability method for small failure probabilities with time-demanding numerical models. Reliability Engineering & System Safety 111, 232–240.CrossRefGoogle Scholar
Fauriat, W., & Gayton, N. (2014). AK-SYS: an adaptation of the AK-MCS method for system reliability. Reliability Engineering & System Safety 123, 137–144.Google Scholar
Hohenbichler, M., & Rackwitz, R. (1983). First-order concepts in system reliability. Structural Safety 1(3), 177–188.Google Scholar
Hohenbichler, M., & Rackwitz, R. (1988). Improvement of second-order reliability estimates by importance sampling. Journal of Engineering Mechanics 114(12), 2195–2199.CrossRefGoogle Scholar
Hu, Z., & Du, X. (2015). A random field approach to reliability analysis with random and interval variables. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering 1(4), 041005.Google Scholar
Hu, Z., & Mahadevan, S. (2015 a). Global sensitivity analysis-enhanced surrogate (GSAS) modeling for reliability analysis. Structural and Multidisciplinary Optimization. Advance online publication.Google Scholar
Hu, Z., & Mahadevan, S. (2015 b). Time-sependent system reliability analysis using random field discretization. Journal of Mechanical Design 137(10), 101404.CrossRefGoogle Scholar
Hu, C., & Youn, B.D. (2011). Adaptive-sparse polynomial chaos expansion for reliability analysis and design of complex engineering systems. Structural and Multidisciplinary Optimization 43(3), 419–442.Google Scholar
Kopp, G., Ferre, J., & Giralt, F. (1997). The use of pattern recognition and proper orthogonal decomposition in identifying the structure of fully-developed free turbulence. Journal of Fluids Engineering 119(2), 289–296.Google Scholar
Koprinarov, I., Hitchcock, A., McCrory, C., & Childs, R. (2002). Quantitative mapping of structured polymeric systems using singular value decomposition analysis of soft X-ray images. Journal of Physical Chemistry B 106(21), 5358–5364.CrossRefGoogle Scholar
Liang, J., Mourelatos, Z.P., & Nikolaidis, E. (2007). A single-loop approach for system reliability-based design optimization. Journal of Mechanical Design 129(12), 1215–1224.CrossRefGoogle Scholar
Lophaven, S.N., Nielsen, H.B., & Søndergaard, J. (2002). DACE—A Matlab Kriging toolbox, version 2.0. Accessed at http://www2.imm.dtu.dk/projects/dace/ Google Scholar
Mahadevan, S., & Haldar, A. (2000). Probability, Reliability and Statistical Method in Engineering Design. New York: Wiley.Google Scholar
Mathworks Inc. (1998). Mathworks User's Guide. Natick, MA: Author.Google Scholar
McDonald, M., & Mahadevan, S. (2008). Design optimization with system-level reliability constraints. Journal of Mechanical Design 130(2), 021403.Google Scholar
Mori, Y., & Ellingwood, B. R. (1993). Time-dependent system reliability analysis by adaptive importance sampling. Structural Safety 12(1), 59–73.Google Scholar
Myers, D.E. (1982). Matrix formulation of co-kriging. Journal of the International Association for Mathematical Geology 14(3), 249–257.Google Scholar
Palmer, J.A., Mejia-Alvarez, R., Best, J.L., & Christensen, K.T. (2012). Particle-image velocimetry measurements of flow over interacting barchan dunes. Experiments in Fluids 52(3), 809–829.CrossRefGoogle Scholar
Rasmussen, C.E. (2006). Gaussian Processes for Machine Learning. Cambridge, MA: MIT Press.Google Scholar
Reams, R. (1999). Hadamard inverses, square roots and products of almost semidefinite matrices. Linear Algebra and Its Applications 288, 35–43.Google Scholar
Sanchez, E., Pintos, S., & Queipo, N.V. (2008). Toward an optimal ensemble of kernel-based approximations with engineering applications. Structural and Multidisciplinary Optimization 36(3), 247–261.Google Scholar
Schueremans, L., & Van Gemert, D. (2005). Benefit of splines and neural networks in simulation based structural reliability analysis. Structural Safety 27(3), 246–261.CrossRefGoogle Scholar
Song, J., & Der Kiureghian, A. (2003). Bounds on system reliability by linear programming. Journal of Engineering Mechanics 129(6), 627–636.Google Scholar
Viana, F.A., & Haftka, R.T. (2008). Using multiple surrogates for metamodeling. Proc. 7th ASMO-UK/ISSMO Int. Conf. Engineering Design Optimization, pp. 1–18, Bath, UK, July 7–8.Google Scholar
Viana, F.A., Haftka, R.T., & Steffen, V. Jr. (2009). Multiple surrogates: how cross-validation errors can help us to obtain the best predictor. Structural and Multidisciplinary Optimization 39(4), 439–457.CrossRefGoogle Scholar
Wang, P., Hu, C., & Youn, B.D. (2011). A generalized complementary intersection method (GCIM) for system reliability analysis. Journal of Mechanical Design 133(7), 071003.Google Scholar
Wong, T.-T., Luk, W.-S., & Heng, P.-A. (1997). Sampling with Hammersley and Halton points. Journal of Graphics Tools 2(2), 9–24.CrossRefGoogle Scholar
Youn, B.D., Choi, K., Yang, R.-J., & Gu, L. (2004). Reliability-based design optimization for crash worthiness of vehicle side impact. Structural and Multidisciplinary Optimization 26(3–4), 272–283.Google Scholar
Youn, B.D., Hu, C., & Wang, P. (2011). Resilience-driven system design of complex engineered systems. Journal of Mechanical Design 133(10), 101011.CrossRefGoogle Scholar
Youn, B.D., & Wang, P. (2009). Complementary intersection method for system reliability analysis. Journal of Mechanical Design 131(4), 041004.CrossRefGoogle Scholar
Youn, B.D., Wang, P., Xi, Z., & Gorsich, D.J. (2007). Complementary interaction method (CIM) for system reliability analysis. Proc. ASME 2007 Int. Design Engineering Technical Confs. Computers and Information in Engineering Conf., pp. 1285–1295. New York: American Society of Mechanical Engineers.Google Scholar
Zou, T., & Mahadevan, S. (2006). A direct decoupling approach for efficient reliability-based design optimization. Structural and Multidisciplinary Optimization 31(3), 190–200.Google Scholar